Cruciform

A plane curve also called the Cross Curve and Policeman on Point Duty Curve (Cundy and Rollett 1989). It is given by the equation

 (1)

which is equivalent to
 (2)

 (3)

or, rewriting,
 (4)

In parametric form,
 (5) (6)

The Curvature is
 (7)

References

Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., p. 71, 1989.

Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 127 and 130-131, 1972.